摘要

文章涉及了两个时间序列的任务：forecasting，imputation.
对于预测任务：通过将时间序列编码为一系列数字，可以将时间序列预测任务转化为文本里面的next-token预测任务。在大规模预训练语言模型的基础上，文章提出了一些方法用于有效编码时间序列数据，并将离散分布的编码转换成灵活的连续分布（分布转换部分涉及到诸多统计学知识）。
在数值补全任务中，文章展示了语言模型（LLMs）如何通过非数值文本自然处理缺失数据，无需插补，如何适应文本侧面信息，并回答问题以帮助解释预测。

方法

文章提出了LLMTime模型


https://unit8co.github.io/darts/generated_api/darts.datasets.html

源码

需要用到openai 密钥，所以没有完全跑通openai.api_key = os.environ[‘OPENAI_API_KEY’]

1.利用darts加载数据集（需要挂梯子）

train:val:test=3:1:1
还有其他的一些数据集：

2.模型预测，llm完全不需要训练，直接将时间序列输入llm进行预测

感觉完全不需要重新训练和微调就有点离谱

serialize：处理输入数据

（1）scaler 放缩

（2）数字到字符串映射
vec_num2repr(val, base, prec, max_val)#将数字转化为指定进制和精度的表示

def vec_num2repr(val, base, prec, max_val):
    """
    将数字转换为指定进制和精度的表示
    Convert numbers to a representation in a specified base with precision.

    Parameters:
    - val (np.array): The numbers to represent.
    - base (int): The base of the representation.
    - prec (int): The precision after the 'decimal' point in the base representation.
    - max_val (float): The maximum absolute value of the number.

    Returns:
    - tuple: Sign and digits in the specified base representation.
    
    Examples:
        With base=10, prec=2:
            0.5   ->    50
            3.52  ->   352
            12.5  ->  1250
    """
    base = float(base)
    bs = val.shape[0]
    sign = 1 * (val >= 0) - 1 * (val < 0)#if val[i]>0,sign[i]=1 else sign[i]=-1
    val = np.abs(val)
    max_bit_pos = int(np.ceil(np.log(max_val) / np.log(base)).item()) #计算最大位数

    #使用循环迭代计算整数部分的每一位数字，存储在before_decimals中。每次迭代将相应的位数从val中减去。
    before_decimals = []
    for i in range(max_bit_pos):
        digit = (val / base**(max_bit_pos - i - 1)).astype(int)
        before_decimals.append(digit)
        val -= digit * base**(max_bit_pos - i - 1)

    before_decimals = np.stack(before_decimals, axis=-1)

    if prec > 0:
        after_decimals = []
        for i in range(prec):
            digit = (val / base**(-i - 1)).astype(int)
            after_decimals.append(digit)
            val -= digit * base**(-i - 1)

        after_decimals = np.stack(after_decimals, axis=-1)
        digits = np.concatenate([before_decimals, after_decimals], axis=-1)
    else:
        digits = before_decimals
    #包含符号和数字的元组，其中符号是一个数组（sign），数字是一个二维数组（digits），表示了数字在指定进制下的表示。
    return sign, digits

（3）添加分隔符：
def tokenize(arr):
return ‘’.join([settings.bit_sep+str(b) for b in arr])

（4）长度对齐
truncate_input(input_arr, input_str, settings, model, steps)
#截断输入以适应给定模型的最大上下文长度

预测：将序列输入到GPT模型

模型：可以看到处理过的输入input_str和提前预设好的chatgpt_sys_messsage信息、extra_input 信息拼接成为发送给GPT的messages。

model
if model in ['gpt-3.5-turbo','gpt-4']:
    chatgpt_sys_message = "You are a helpful assistant that performs time series predictions. The user will provide a sequence and you will predict the remaining sequence. The sequence is represented by decimal strings separated by commas."
    extra_input = "Please continue the following sequence without producing any additional text. Do not say anything like 'the next terms in the sequence are', just return the numbers. Sequence:\n"
    response = openai.ChatCompletion.create(
        model=model,
        messages=[
                {"role": "system", "content": chatgpt_sys_message},
                {"role": "user", "content": extra_input+input_str+settings.time_sep}
            ],
        max_tokens=int(avg_tokens_per_step*steps), 
        temperature=temp,
        logit_bias=logit_bias,
        n=num_samples,
    )
    return [choice.message.content for choice in response.choices]

对于GPT返回的Response

deserialize：处理GPT返回的信息

pred = handle_prediction(deserialize_str(completion, settings, ignore_last=False, steps=steps), expected_length=steps, strict=strict_handling)

从上面代码看出，先是deserialize

def deserialize_str(bit_str, settings: SerializerSettings, ignore_last=False, steps=None):
    """
    Deserialize a string into an array of numbers (a time series) based on the provided settings.

    Parameters:
    - bit_str (str): String representation of an array of numbers.
    - settings (SerializerSettings): Settings for deserialization.
    - ignore_last (bool): If True, ignores the last time step in the string (which may be incomplete due to token limit etc.). Default is False.
    - steps (int, optional): Number of steps or entries to deserialize.

    Returns:
    - None if deserialization failed for the very first number, otherwise 
    - np.array: Array of numbers corresponding to the string.
    """
    # ignore_last is for ignoring the last time step in the prediction, which is often a partially generated due to token limit
    orig_bitstring = bit_str
    bit_strs = bit_str.split(settings.time_sep)
    # remove empty strings
    bit_strs = [a for a in bit_strs if len(a) > 0]
    if ignore_last:
        bit_strs = bit_strs[:-1]
    if steps is not None:
        bit_strs = bit_strs[:steps]
    vrepr2num = partial(vec_repr2num,base=settings.base,prec=settings.prec,half_bin_correction=settings.half_bin_correction)
    max_bit_pos = int(np.ceil(np.log(settings.max_val)/np.log(settings.base)).item())
    sign_arr = []
    digits_arr = []
    try:
        for i, bit_str in enumerate(bit_strs):
            if bit_str.startswith(settings.minus_sign):
                sign = -1
            elif bit_str.startswith(settings.plus_sign):
                sign = 1
            else:
                assert settings.signed == False, f"signed bit_str must start with {settings.minus_sign} or {settings.plus_sign}"
            bit_str = bit_str[len(settings.plus_sign):] if sign==1 else bit_str[len(settings.minus_sign):]
            if settings.bit_sep=='':
                bits = [b for b in bit_str.lstrip()]
            else:
                bits = [b[:1] for b in bit_str.lstrip().split(settings.bit_sep)]
            if settings.fixed_length:
                assert len(bits) == max_bit_pos+settings.prec, f"fixed length bit_str must have {max_bit_pos+settings.prec} bits, but has {len(bits)}: '{bit_str}'"
            digits = []
            for b in bits:
                if b==settings.decimal_point:
                    continue
                # check if is a digit
                if b.isdigit():
                    digits.append(int(b))
                else:
                    break
            #digits = [int(b) for b in bits]
            sign_arr.append(sign)
            digits_arr.append(digits)
    except Exception as e:
        print(f"Error deserializing {settings.time_sep.join(bit_strs[i-2:i+5])}{settings.time_sep}\n\t{e}")
        print(f'Got {orig_bitstring}')
        print(f"Bitstr {bit_str}, separator {settings.bit_sep}")
        # At this point, we have already deserialized some of the bit_strs, so we return those below
    if digits_arr:
        # add leading zeros to get to equal lengths
        max_len = max([len(d) for d in digits_arr])
        for i in range(len(digits_arr)):
            digits_arr[i] = [0]*(max_len-len(digits_arr[i])) + digits_arr[i]
        return vrepr2num(np.array(sign_arr), np.array(digits_arr))
    else:
        # errored at first step
        return None

计算损失函数

# Compute NLL/D on the true test series conditioned on the (truncated) input series
if nll_fn is not None:
    BPDs = [nll_fn(input_arr=input_arrs[i], target_arr=test[i].values, settings=settings, transform=scalers[i].transform, count_seps=True, temp=temp) for i in range(len(train))]
    out_dict['NLL/D'] = np.mean(BPDs)